Question

In: Finance

Expected return and standard deviation. Use the following information to answer the questions.   State of   Economy...

Expected return and standard deviation.

Use the following information to answer the questions.

  State of

  Economy

Probability

of State

Return on

Asset A in

State

Return on

Asset B in

State

Return on

Asset C in

State

  Boom

0.34

0.02

0.22

0.35

  Normal

0.52

0.02

0.09

0.23

  Recession

0.14

0.02

−0.02

−0.21

a.  What is the expected return of each​ asset?

b.  What is the variance of each​ asset?

c.  What is the standard deviation of each​ asset?

​Hint: Make sure to round all intermediate calculations to at least seven​ (7) decimal places. The input​ instructions, phrases in parenthesis after each answer​ box, only apply for the answers you will type.


Solutions

Expert Solution

Solution:

a. The expected return for each asset is calculated by multiplying the probabilities of return with the return on each asset.

= 0.34*0.02 + 0.52*0.02 + 0.14*0.02

= 0.02 or 2%

= 0.34*0.22 + 0.52*0.09 + 0.14*(-0.02)

= 0.1188 or 11.88%

= 0.34*0.35 + 0.52*0.23 + 0.14*(-0.21)

= 0.2092 or 20.92%

---------------------------------------------------------------------------------------------------------------------------------------------------------------------

b. The variance for each asset is calculated using the following formula

= 0.34*(0.02 - 0.02)^2 + 0.52*(0.02 - 0.02)^2 + 0.14*(0.02 - 0.02)^2

= 0

= 0.34*(0.22 - 0.1188)^2 + 0.52*(0.09 - 0.1188)^2 + 0.14*(-0.02 - 0.1188)^2

= 0.00661056 or 66.1056 (%)^2

= 0.34*(0.35 - 0.2092)^2 + 0.52*(0.23 - 0.2092)^2 + 0.14*(-0.21 - 0.2092)^2

= 0.003156736 or 315.6736 (%)^2

---------------------------------------------------------------------------------------------------------------------------------------------------------------------

c. The standard deviation for each asset is the square root of the variance

0 = 0

66.1056 = 8.13%

315.6736 = 17.77%


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